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1
Bundle achiote seeds, peppercorns, and bay leaves in cheesecloth and tie closed with kitchen twine; set sachet aside.
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2
Preheat oven to 225u00b0F. Heat 1 Tbsp. oil in a large Dutch oven or wide heavy pot over medium-high. Season oxtails generously with salt and pepper. Cook half of oxtails until browned all over, 8-12 minutes; transfer to a platter. Add 1 Tbsp. oil to pot; cook remaining oxtails. Pour off all but 3 Tbsp. fat from pot. (If pot is scorched, clean and start with 3 Tbsp. fresh oil.)
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3
Return pot to medium-high heat. Cook chopped onion, carrots, celery, and mushrooms, stirring often, until lightly browned and very soft, 12-15 minutes. Add wine; cook, scraping up any browned bits, until almost completely evaporated, about 5 minutes. Add 2 quarts water and reserved sachet. Bring to a vigorous boil; cook 1 minute. Return oxtails to pot (add water if needed to just cover). Reduce heat so liquid is simmering gently, cover, and transfer to oven. Braise, checking every 2 hours and adding more water if needed to keep oxtails barely submerged, until meat is just about falling off the bone, 6-8 hours. Let cool. Skim off fat; discard. (Or, ideally, chill overnight and scrape off fat before proceeding.)
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4
Remove oxtails from pot; pull meat from bones. Discard bones (or save some meaty bones for serving). Strain braising liquid into a large bowl. You should have 6-8 cups; simmer to reduce further or add water if needed. Discard solids.
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5
Clean pot and heat remaining 2 Tbsp. oil over medium. Cook sliced onion, garlic, and garlic chives, stirring often, until onion is translucent, about 5 minutes. Add bok choy, eggplant, taro (if using), and long beans; cook, stirring often, until just beginning to soften, about 5 minutes. Add braising liquid and bring to a simmer; season with salt. Cook until vegetables are halfway tender, 6-8 minutes. Stir in peanut butter to dissolve, then add meat. Cook just until meat is heated through, vegetables are tender, and flavors have melded, about 5 minutes. Season with more salt if needed.
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6
Divide kare-kare among bowls; top with peanuts and red chile. Serve with shrimp paste.